West Ham sit eighth in the Premier League, five points adrift of sixth-placed Tottenham.
A 4-0 drubbing at the hands of West Brom in the FA Cup fifth round at the weekend led to apologies for the nature of the defeat, but Downing insists West Ham - who face Tottenham on Sunday - are more than capable of sustaining their push for a place in Europe.
"If we get a good result against Tottenham, we can put it to bed and have a good finish to the season," he said. "If you told the fans we get knocked out of the cup but finish in Europe, they will take that.
"We owe Tottenham one after they beat us in the last minute on the opening day of the season, and I don't accept they’re going to finish above us.
"They spent a lot of money and man-for-man I don't think they're any better than us.
"We don't want to waste all the good work, and all the top teams we've beaten, over the first six months of the season."
